Sound velocity and dimensional crossover in a superfluid Fermi gas in an optical lattice

We study the sound velocity in cubic and noncubic three-dimensional optical lattices. We show how the van Hove singularity of the free Fermi gas is smoothed by interactions and eventually vanishes when interactions are strong enough. For noncubic lattices, we show that the speed of sound (Bogoliubov-Anderson phonon) shows clear signatures of dimensional crossover both in the one- and two-dimensional limits.